[PRL] point-free set notation

David Herman dherman at ccs.neu.edu
Sat Jan 9 16:33:32 EST 2010


I assume that notation works on both sides? So:

     {n}(>) = {m | n > m}
     (>){n} = {m | m > n}

Thanks,
Dave

On Jan 9, 2010, at 1:19 PM, Aaron Turon wrote:

> It sounds like you want the relational image.  If R is a binary
> relation and X is a set, then RX = {a : a R b, b in X} and XR = {b : a
> R b, a in X}.
>
> So for your example you could write (>){n}, often abbreviated by >n
> when the types are clear.
>
> On Sat, Jan 9, 2010 at 3:43 PM, David Herman <dherman at ccs.neu.edu>  
> wrote:
>> In Haskell, you can curry a binary operator to define a function
>> without naming the missing argument:
>>
>>     (+n) === \m -> (m+n)
>>
>> Is there an analogous notation in math for constructing a set based  
>> on
>> a binary relation with an omitted element? For example, I'd like to  
>> be
>> able to define the set of integers > n like:
>>
>>     { -- > n } === { m | m > n }
>>
>> or something like that. (I'm aware that generally this is a type-
>> ambiguous notation, but for my purposes the meta-variables involved
>> are enough to disambiguate.)
>>
>> Thanks,
>> Dave
>>
>>
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